Can someone help me with 16 and 20? If you’re supposed to write a contrapositive and inverse, but the word not is already in the statement, what do you do?
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Related Questions
sharon drives 3 miles to every 2 miles driven by steve how far does sharon drive if the journey is 250 miles
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250 / 5 = 50
so sharon drives 3*50 = 150 miles and steve drives 100.
750/2=375
Jen bought 5 cds for 57.50. What was the unit price
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$11.50
Hope this helps!
what is the solution of x^2+x-6≤0?
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x^2 + x - 6 = (x + 3) (x - 2)
So, can solve (x + 3)(x - 2) ≤ 0
The condition for the product of two factors be zero or negative is that the both are zero or have different signs (one positive and the other negative)
a) when x + 3 ≤ 0 and x - 2 ≥ 0
x + 3 ≤ 0 => x ≤ - 3
x - 2 ≥ 0 => x ≥ 2
Given that it is imposible that x be less or equal tha - 3 and greaer or equal than 2, this solution is empy.
b) when x + 3 ≥ 0 and x - 2 ≤ 0
x + 3 ≥ 0 => x ≥ - 3
x - 2 ≤ 0 => x ≤ 2
Solution: - 3 ≤ x ≤ 2 or [-3,2]
assume f(x)=4x+8 and g(x)=5. what is the value of (golf)(-1)
idk what is it, show work plz?
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The population of a community is known to increase at a rate proportional to the number of people present at time t. if an initial population p0 has doubled in 7 years, how long will it take to triple? (round your answer to one decimal place.)
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To determine how long it will take for the population to triple, we need to solve the equation 3P0 = P0e^(rt) for t. Rounding the answer to one decimal place, it will take approximately 10.1 years for the population to triple.
Explanation:To solve this problem, we can use the equation P = P0e^(rt), where P is the population at a given time, P0 is the initial population, e is the base of the natural logarithm (approximately 2.71828), r is the growth rate, and t is the time in years.
In this case, the population has doubled in 7 years, so we can write the equation as 2P0 = P0e^(r*7). We need to solve for r.
Dividing both sides of the equation by P0 gives us 2 = e^(7r). Taking the natural logarithm of both sides gives us ln(2) = 7r. Solving for r, we find that r ≈ ln(2)/7.
Now, to determine how long it will take for the population to triple, we need to solve the equation 3P0 = P0e^(r*t) for t. Substituting the value of r we found, we get 3 = e^((ln(2)/7)*t). Taking the natural logarithm of both sides to solve for t, we have ln(3) = (ln(2)/7)*t. Solving for t, we find that t ≈ 7 * ln(3)/ln(2). Rounding the answer to one decimal place, it will take approximately 10.1 years for the population to triple.
It takes approximately 11.1 years for the population to triple.
The population growth can be modeled by the exponential function [tex]P(t)=P_0 \times e^{k t}[/tex], where [tex]P_0[/tex] is the initial population, k is the growth rate, and t is time.
In this case, since the population doubles in 7 years, we have the relationship P(7) = 2 x [tex]P_0[/tex].
[tex]P(7)=P_0 \times e^{7 k}[/tex]
[tex]2 \times P_0=P_0 \times e^{7 k}[/tex]
Divide both sides by [tex]P_0[/tex].
[tex]2=e^{7 k}[/tex]
Take the natural logarithm (ln) of both sides to solve for k:
ln(2) = 7k
[tex]k=\frac{\ln (2)}{7}[/tex]
Now that we have the growth rate k, we can use it to find the time it takes for the population to triple.
[tex]P(t)=P_0 \times e^{k t}[/tex]
For tripling, [tex]P(t)=3 \times P_0[/tex].
[tex]3 \times P_0=P_0 \times e^{k t}[/tex]
[tex]3=e^{k t}[/tex]
Take the natural logarithm again:
ln(3) = kt
[tex]t=\frac{\ln (3)}{k}[/tex]
Substitute the value of k we found earlier:
[tex]t=\frac{\ln (3)}{\frac{\ln (2)}{7}}[/tex]
Using natural logarithm values:
[tex]t \approx \frac{1.0986}{\frac{0.6931}{7}}[/tex]
[tex]t \approx \frac{1.0986}{0.0990}[/tex]
t ≈ 11.09
Use the premises and conclusion to answer the questions.
Premises:
If a quadrilateral has two pairs of parallel sides, then it is a parallelogram.
If a quadrilateral is a parallelogram, then its opposite angles are congruent.
Conclusion:
If a quadrilateral has two pairs of parallel sides, then its opposite angles are congruent.
Which statement best describes this argument?
The argument is valid by the law of syllogism.
The argument is invalid because the conclusion does not follow the premises.
The argument is valid by the law of detachment.
The argument is invalid because the premises are not true.
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Answer:
The argument is valid by the law of syllogism.
Step-by-step explanation:
The law of syllogism is also called the law of transitivity. It is based on the transitive property, which states "if a = b and b = c, then a = c."
In our problem, our statement a would be "A quadrilateral has two pairs of parallel sides". Our statement b would be "It is a parallelogram." Our statement c would be "Its opposite angles are congruent."
That would make "if a = b"
"If a quadrilateral has two pairs of parallel sides it is a parallelogram."
Then "b = c" would be
"If a quadrilateral is a parallelogram, its opposite angles are congruent."
"a = c" would then be
"If a quadrilateral has two pairs of parallel sides its opposite angles are congruent."
This is the conclusion we were given, so this is the law of syllogism.
Six identically shaped place mats, marked a, b, c, d, e and f, are piled neatly in a stack. how many arrangements are possible if a and b must touch each other?
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1. A, b, c
2. A, b, d
3. A, b, e
4. C, a, b
5. D, a, b
6. E, a, b
Hope I helped!
275 mm = _____ cm
954 g = _____ kg
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1mm = 0.1cm
275 * 0.1 = 27.5 cm
1 g = 0.001 kg
954 x 0.001 = 0.954 kg
954g=0.945kg
Hope this helped
Sawyer’s mom paid $1.50 for a 3/4 pound box of cereal. How much is that per pound?
A.$1.50
B.$1.75
C.$2.00
D.$2.50
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Sue has 18 sweets. tony has 18 sweets.sue gives tony x sweets. Sue then eats 5 sweets. Tony then eats half of his sweets. Write expressions for the number of sweets sue and tony have now
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The expressions for the number of sweet Sue and Tony have are 13 - x and
18 + x / 2 respectively
Sue has 18 sweet.
Tony has 18 sweet.
Sue gives Tony x sweet . Sue sweet will be
18 - xSue then eats 5 sweets then his sweet will be
18 - 5 - x = 13 - xTony collected x sweet from Sue. His sweet will be
18 + xTony ate half of his sweets . His remaining sweet will be
18 + x / 2The expression for Sue sweets is : 13 - x
The expression for Tony sweets is : 18 + x / 2
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Expressions for the number of sweets sue and tony have now :
Sue: 13 - x sweets
Tony: (3/2)x + 18 sweets
Here are the expressions for the number of sweets Sue and Tony have now:
Sue: 18 - x - 5 = 13 - x
Tony: 18 + x - (1/2)x = (3/2)x + 18
Here's a breakdown of the calculations:
Sue's sweets:
Sue starts with 18 sweets.
She gives Tony x sweets.
She then eats 5 of her sweets.
Therefore, Sue now has 18 - x - 5 sweets, which can be simplified to 13 - x.
Tony's sweets:
Tony starts with 18 sweets.
Sue gives him x sweets.
He then eats half of his sweets.
Since Tony eats half of his sweets, he is left with (1/2) of his sweets. Therefore, Tony now has 18 + x - (1/2)x sweets, which can be simplified to (3/2)x + 18.
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The measure of ∠AKG is 133°.
What is m∠AKD?
Enter your answer in the box.
m∠AKD =
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133° = mes ∠ AKD + 87°
133° - 87° = mes ∠AKD
∠AKD = 46°
To find m∠AKD, subtract the measure of ∠AKG from 180 degrees.
Explanation:To find the measure of ∠AKD, we need to use the fact that the sum of the measures of angles in a triangle is 180 degrees. Since we know that ∠AKG is 133 degrees, we can subtract this from 180 to find the remaining angle.
180 - 133 = 47 degrees
Therefore, m∠AKD = 47 degrees.
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Identify where the given information is sufficient for graphing a linear equation. Check all that apply.
A.one point and the slope of the line
B.one point
C.one of the intercepts and the slope of the line
D.both the intercepts
E.two points
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To graph a linear equation, you need at least two pieces of information: the slope and a point, both intercepts, or two points. One point and the slope, or one intercept and the slope, are also sufficient to graph a linear equation.
Explanation:For graphing a linear equation, there are several options that provide sufficient information:
A. One point and the slope of the lineC. One of the intercepts and the slope of the lineD. Both the interceptsE. Two pointsTo graph a linear equation, you need at least two pieces of information, such as the slope and a point or both intercepts. Having two points is also sufficient since it helps determine the slope. Having just one point or one intercept along with the slope is also enough to graph the line.
Round 156, 782 to nearest thousand and the nearest ten thousand.
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156, 782 rounded to the nearest ten thousand is 160,000.
The answer is 167,000 because if you round to the 6,782 up it is 7,000. If you round 57,782 up it is 60,000. so then just add those 2 together and plug the 100,000 into it.
How to find the other endpoint with the given endpoint and midpoint?
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A football team lost 5 yards on one play and gained 12 yards on the next play. write a sum of integers to find the overall change in field position. explain your answer
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-5 + 12 = 7...overall change is 7
To the nearest tenth, find the perimeter of ∆ABC with vertices A(2,4), B(-2,1) and C(2,1). Show your work.
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The distance between two coordinates (x₁, y₁) and (x₂, y₂) is given by the formula
[tex]d= \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}} [/tex]
Because the triangle is a right angle (indicated by the figure), we can determine the lengths of BC and AC easily.
The length of BC is the change in the x-coordinates, and AC is the change in the y-coordinates.
BC = 2 - (-2) = 4
AC = 4 - 1 = 3
To find AB, use the distance formula (the same as the Pythagorean theorem).
AB = √[(2-(2)) ²+ (4-1)² ] = √(4²+3²) = √25 = 5
The area of the triangle is (1/2)*BC*AC = (1/2)*4*3 = 6
Answer: 6
A quota is when one country
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This is done in order to give prominence to domestic suppliers and producers. If you limit the amount of foreign goods, then its price will rise, which will make consumers buy more domestic goods and thus help develop domestic trade.
In 2003, the population of an african country was about 12 million people, which is 3 million more than 2 times the population in 1950. enter and solve an equation to find the approximate population p (in millions) in 1950. an equation is . the approximate population in 1950 was million people.
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12 - 3 = 2p
9 = 2p
9/2 = p
4.5 = p......so the population in 1950 was approximately 4.5 million people
Answer:
3 million
Step-by-step explanation:
Prove that composition of injective functions is injective. prove that composition of surjective functions is surjective.
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f(x) is injective
f(a) = f(b) <--> a = b
g(x) is injective
g(a) = g(b) <--> a = b
prove f(g(x)) is injective
f(g(a)) = f(g(b))
f(a) = f(b) ... since g(x) is injective
a = b
So that proves if f(g(a)) = f(g(b)), then a = b
Now go the other direction
a = b
g(a) = g(b)
f(g(a)) = f(g(b))
So that wraps up the sub-proof of "f(g(a)) = f(g(b)) iff a = b"
-------------------------
proving g(f(x)) is injective is going to follow a similar path of steps
------------------------------------------
------------------------------------------
Proof 2: Proving the composition of surjective functions is itself a surjective function.
f(x) is surjective
The range of f(x) is the set of all real numbers
g(x) is surjective
The range of g(x) is the set of all real numbers
f(g(x)) is also surjective because of property 1 listed above. The range of f(x) is the set of all real numbers. The fact that g(x) represents all reals as well means that we touch all of the inputs needed to generate all the outputs for f(x).
-------------------------
Proving g(f(x)) to be surjective follows a similar path.
It is found that the composition of injective functions is injective.
What is an injective function?An injective function is not a surjective function. This means that we want a function that has a unique output for each input, that doesn't cover the natural numbers.
Proof 1: Proving the composition of injective functions is injective.
f(x) is injective
f(a) = f(b)
a = b
Thus g(x) is injective
g(a) = g(b)
a = b
To prove; f(g(x)) is injective
f(g(a)) = f(g(b))
f(a) = f(b)
Since, g(x) is injective
a = b
Therefore, if f(g(a)) = f(g(b)), then a = b
That proving g(f(x)) is injective is going to follow a similar path of steps.
Proof 2: Proving the composition of surjective functions is surjective.
f(x) is surjective
The range of the function of x is the set of all real numbers
g(x) is surjective
The range of the function of x is the set of all real numbers
f(g(x)) is also surjective. The range of f(x) is the set of all real numbers. where g(x) represents all reals as well means that we touch all of the inputs needed to generate all the outputs for f(x).
Proving g(f(x)) to be surjective follows a similar path.
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Standard form of 5y=35+10x
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Answer:
[tex]5y - 10x - 35 = 0[/tex]
Step-by-step explanation:
The standard way to write a linear relationship between the x and y variables is through a homogeneous equation as a combination of the x and y variables with real coefficients. The form is given by the expression:
[tex]ax + by + c = 0[/tex]
The equation [tex]5y = 35 + 10x[/tex] can be written in standard form if terms are transposed, obtaining [tex]5y - 10x - 35 = 0[/tex]
let f(x)=4x-7 and g(x)-5+9x. what are f+g and f-g? what are their domains?
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Which conversion factors can be used to multiply to 4 km/min to get meters per hour?
Select each correct answer.
A. 1 h60min
B. 1000 m1 km
C. 1 km1000 m
D. 60min1 h
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Answer: the answer is B and D
how i know i took a test and it said thes are the anwer
hope this helps you out you a lot
Which equation is equivalent to
X/ +11 = 15
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√x= 15-11 x=16
Which of the symbols does not make the following statement true?
|-1| ___ |1|
>
≤
≥
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Roni and Allie are mowing the grass at the soccer field. Roni has a riding lawn mower and can mow the field in 30 minutes. Allie is pushing a lawn mower and can mow the field in 75 minutes.
If Roni and Allie work together to mow the field, what part of the field would Roni mow?
A. about 0.52 of the field
B. about 0.64 of the field
C. about 0.71 of the field
D. about 0.87 of the field
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Answer: C. about 0.71 of the field
Step-by-step explanation:
Since, Roni can mow the field in 30 minutes.
Thus, the work done by Roni in one day = 1/30
And, Allie can mow the field in 75 minutes.
Thus, the work done by Allie in one day = 1/75
⇒ The total work done by Roni and Allie in one day when they worked simultaneously,
= [tex]\frac{1}{30} + \frac{1}{75}[/tex]
= [tex]\frac{5}{150} + \frac{2}{150}[/tex]
= [tex]\frac{7}{150}[/tex]
[tex]\implies \text{The part of work done by Roni} = \frac{\text{the work done by her in one day}}{\text{Total work they done in one day}}[/tex]
[tex]= \frac{1/30}{7/150}[/tex]
[tex]= \frac{5}{7}=0.714285714\approx 0.71[/tex]
⇒ Option C is correct.
Make a table for a function whose graph has a y-intercept of 4 and a slope of 2/3.
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y = mx + b
where
m is the slope
b is the y-intercept
Substituting the given values, the equation of the line is:
y = 2/3*x + 4
To make a table, substitute arbitrary values of x, so that you would get the corresponding values of y using the equation. The table is shown in the attached picture.
PLEASE HELP ME IN THESE TWO QUESTIONS ASAP! AND YES, I AM GOING TO MARK YOU AS THE BRAINLIEST ANSWER!!!!!
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For that line to be perpendicular to y=-2/5x+6, their slopes should be each other's negative reciprocals.
-2/5 negative reciprocal is 5/2, which is not equal to our calculated 5/3, so (2,2) cannot be the reflected point. Evan was wrong.
Q1-74: AB have slope 6/5, C has -5/6, D 6/5, E -5/6 again.
In a pet store the number of fish is 120 more than three times the number of reptiles. If the pet store has 210 fish, how many reptiles does it have? Write a two step equation to model the scenario. Then solve the question.
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210=3r-120
330=3r
110=r
110 reptiles
Answer:
110
Step-by-step explanation:
Write an equation of an ellipse with vertices of (-3, 0) and (3, 0), and co-vertices (0, -5) and (0, 5). Graph the ellipse.
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This graph is the answer:
What's the greatest common factor of 45,9,63
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Answer:
GCF = 9
Step-by-step explanation: